Method for ascertaining a physical parameter of a gas-charged liquid

ABSTRACT

A method for ascertaining a physical parameter of a liquid, which has a gas charge using a measuring transducer having a measuring tube for conveying the medium. The measuring tube executes oscillations in bending oscillation mode. The method includes: exciting the measuring tube with an eigenfrequency of a bending oscillation mode—or f1-mode, ascertaining a suppressed excitation frequency, at which the oscillation amplitude of the measuring tube is minimum; identifying the frequency as the resonant frequency of the gas-charged liquid; ascertaining a density correction term as a function of the resonant frequency for correcting a preliminary density measured value and/or mass flow correction term as a function of the resonant frequency for correcting a preliminary mass flow rate measured value, and/or ascertaining the velocity of sound in the gas-charged liquid in the measuring tube as a function of the resonant frequency.

The present invention relates to a method for ascertaining a physicalparameter of a gas-charged liquid by means of a measuring transducerhaving at least one measuring tube for conveying the gas-charged liquid,wherein the measuring tube has an inlet side end section and an outletside end section, wherein the measuring transducer has at least oneinlet side securement means and one outlet-side securement means, withwhich the measuring tube is secured, in each case, in one of the endsections, wherein the measuring tube is excitable between the twosecurement means to execute oscillations, wherein from the oscillatorybehavior of the measuring tube mass flow rate and density of thegas-charged liquid are determinable. The measured values for mass flowrate and density have, however, cross sensitivities to velocity of soundin, or compressibility of, the gas-charged liquid, which rises withincreasing gas charge. A compensating of these cross sensitivities is,consequently, desired.

WO 01/01086 A1 discloses a method for compressibility compensation inthe case of mass flow measurement in a Coriolis mass flow measuringdevice. In such case, mass flow measurement is performed in twodifferent modes, of which one is a bending oscillation mode and anothera radial mode. The mass flow rate values ascertained by means of thesetwo modes are compared. Such is, however, a problematic approach, sincethe radial mode oscillations have considerable dependence on the flowprofile and the static pressure. Additionally, more sensors than theusual two are required, in order to be able to register both bendingoscillations as well as also radial mode oscillations. Equally, a morecomplex exciter structure is required.

To a first approximation, a preliminary density value ρ_(i) of agas-charged liquid as a function of eigenfrequency f_(i) of an fi modecan be expressed as:

${\rho_{i} = {c_{0i} + {c_{1i}\frac{1}{f_{i}^{2}}} + {c_{2i}\frac{1}{f_{i}^{4}}}}},$

wherein c_(0i), c_(1i), and c_(2i), are mode dependent coefficients.

The above approximation does not, however, take into consideration theinfluences of the oscillating, gas-charged liquid in the measuring tube.The closer the resonant frequency of the oscillating, gas-charged liquidlies to the eigenfrequency of a bending oscillation mode, the greater isthe influence of the eigenfrequency. Since the resonant frequency lies,usually, above the eigenfrequency of the measuring tubes, the influenceon the f₃-bending oscillation mode is greater than the influence on thef₁-bending oscillation mode. This leads to different preliminary,mode-specific density values, wherein the ratio between the preliminarydensity values provides the possibility of ascertaining and correctingthe influence of the oscillating, gas-charged liquid. Such is describedin DE 10 2015 122 661 A1. When, however, the resonant frequency of thegas-charged liquid agrees with an eigenfrequency of a bendingoscillation mode, such is completely suppressed.

Thus, in this situation, the above described approach does not work.Offenlegungsschrift DE 10 2016 005 547 A1 proposes ascertaining a valuefor the eigenfrequency of the suppressed bending oscillation wanted modein this situation by multiplying the eigenfrequency of the excitablebending oscillation wanted mode by a factor. This enables, indeed, acertain improvement of the accuracy of measurement, but since theinformation to be evaluated is contained in the frequency ratio,ascertaining the unknown second frequency by multiplying a firsteigenfrequency by an estimated, not exactly available factor means thatone lastly influences the measurement result with a more or less thanappropriate model.

It is, therefore, an object of the present invention to provide animproved solution for these situations.

The object is achieved according to the invention by the method asdefined in independent claim 1.

The method of the invention serves for ascertaining a physical parameterof a liquid, which has a gas charge, wherein the gas is presentespecially in the form of bubbles suspended in the liquid, by means of ameasuring transducer having at least one measuring tube for conveyingthe medium, wherein the at least one measuring tube has an inlet sideend section and an outlet side end section, wherein the measuringtransducer has at least one inlet side securement means and oneoutlet-side securement means, with which the measuring tube is secured,in each case, in one of the end sections, wherein the measuring tube isexcitable between the two securement means to execute oscillations in atleast one bending oscillation mode, wherein the method comprises stepsas follows: Exciting the measuring tube with an eigenfrequency of abending oscillation mode, especially the bending oscillation wantedmode, or f₁-mode; ascertaining a suppressed excitation frequency, atwhich the oscillation amplitude of the measuring tube is minimum, ordisappears; identifying the suppressed excitation frequency as theresonant frequency of the gas-charged liquid; ascertaining a densitycorrection term as a function of the resonant frequency for correcting apreliminary density measured value and/or mass flow correction term as afunction of the resonant frequency for correcting a preliminary massflow rate measured value, and/or ascertaining the velocity of sound inthe gas-charged liquid in the measuring tube as a function of theresonant frequency.

In an additional development of the invention, the suppressed excitationfrequency is ascertained by sampling a frequency range, wherein thesampling of the frequency range comprises especially the outputting ofexcitation signals having a sequence of excitation frequencies in thefrequency range for exciting measuring tube oscillations, and theregistering of the frequency dependent oscillation amplitudes.

In an additional development of the invention, the suppressed excitationfrequency is ascertained by: Exciting oscillations with an excitationsignal in the form of white noise; registering resulting deflection ofthe measuring tube in the time domain; transforming the registration inthe time domain into the frequency domain, especially by means of anFFT; ascertaining frequency of an amplitude minimum; and identifying theascertained frequency as the suppressed excitation frequency.

In an additional development of the invention, the method furtherincludes ascertaining a preliminary density measured value and/or apreliminary mass flow rate measured value at the eigenfrequency of theexcited bending oscillation mode, and ascertaining a corrected densitymeasured value and/or a corrected mass flow rate measured value usingthe density correction term and/or the mass flow correction term,wherein the density correction term and/or the mass flow correction termare, or is, a function of the resonant frequency and the eigenfrequencyof the excited bending oscillation mode, at which the preliminarydensity measured value and/or the preliminary mass flow rate measuredvalue were, or was, ascertained.

In an additional development of the invention, the density correctionterm K_(i) for a preliminary density value and/or the mass flowcorrection term are, or is, a function of a quotient of the resonantfrequency of the gas-charged liquid and the eigenfrequency of theexcited bending oscillation mode, at which the preliminary densitymeasured value and/or mass flow rate measured value were, or was,ascertained.

In an additional development of the invention, the density correctionterm K_(i) for the preliminary density values ρ_(i) based on theeigenfrequency of the f_(i)-mode has the following form:

${K_{i}\mspace{14mu}\text{:=}\mspace{14mu}\left( {1 + \frac{r}{\left( \frac{f_{res}}{f_{i}} \right)^{2} - b}} \right)},{wherein}$$\rho_{corr}\mspace{14mu}\text{·=}\mspace{14mu}\frac{\rho_{i}}{K_{i}}$

wherein r is a media independent constant, f_(res) is the resonantfrequency of the gas-charged liquid, f_(i) is the eigenfrequency of theexcited bending oscillation mode, ρ_(corr), ρ_(i) are the corrected andthe preliminary densities, and b is a scaling constant. In an embodimentof this additional development: r/b<1, especially r/b<0.9, whereinespecially: b=1.

In an additional development of the invention, g is a proportionalityfactor between a resonant frequency f_(res) of the gas-charged liquidand the velocity of sound in the gas-charged liquid and depends on thediameter of the measuring tube, thus,

${c = \frac{f_{res}}{g}},$

and a value of the velocity of sound ascertained with the equation isoutput.

In an additional development of the invention, the preliminary densityvalue is determined based on the eigenfrequency of the f_(i)-mode bymeans of a polynomial in 1/f_(i), especially in (1/f_(i))², wherein thecoefficients of the polynomial are mode dependent.

In an additional development of the invention, a density error E_(ρi) ofa preliminary density value based on the eigenfrequency of the fi modeis:

E _(ρi) :=K _(i)−1,

wherein a mass flow rate error E_(m) of a preliminary mass flow ratevalue is proportional to the density error E_(ρ1) of the firstpreliminary density value, thus:

E _(m) :=k·E _(ρ1),

wherein the proportionality factor k amounts to not less than 1.9 and nomore than 2.1,

wherein the proportionality factor k especially amounts to 2,

wherein the mass flow correction term K_(m) for the mass flow rate is:

K _(m):=1+E _(m),

wherein the corrected mass flow rate {dot over (m)}_(corr) is

${{\overset{.}{m}}_{corr}\mspace{14mu}\text{·=}\mspace{14mu}\frac{{\overset{.}{m}}_{v}}{K_{m}}},$

wherein {dot over (m)}_(v) is the preliminary mass flow rate value.

In an additional development of the invention, the f₁-mode and thef₃-mode are excited, wherein their eigenfrequencies are ascertained,wherein as a function of the ascertained eigenfrequencies a frequencyrange is established, in which the suppressed excitation frequency is tobe sought.

In an additional development of the invention, a reference density,especially for the liquid phase of the medium, is provided, wherein as afunction of the reference density and, in given cases, theeigenfrequency of the f₁-mode a frequency range is established, in whichthe suppressed excitation frequency is to be sought.

The invention will now be explained in greater detail based on theexample of an embodiment illustrated in the drawing.

The figures of the drawing show as follows:

FIG. 1 a flow diagram of an example of an embodiment of the method ofthe invention;

FIG. 2a a flow diagram of a first embodiment for ascertaining asuppressed excitation frequency in the example of an embodiment of FIG.1; and

FIG. 2b a flow diagram of a second embodiment for ascertaining asuppressed excitation frequency in the example of an embodiment of FIG.1

The example of an embodiment of a method 100 of the invention shown inFIG. 1 for determining density value begins in a step 110 with theexciting of a bending oscillation mode, especially the f₁-mode, which isalso referred to as bending oscillation wanted mode.

Then there occurs the determining of the eigenfrequency of the excitedbending oscillation mode, for example, of the f₁-mode, for example, as aresult of maximizing the ratio of the oscillation amplitude to the modespecific excitation power. By varying the excitation frequencies, thesought eigenfrequencies can be ascertained.

-   -   Based on the ascertained eigenfrequency f_(i), then in a step        120 a preliminary density measured value ρ₁ is determined as:

${\rho_{i} = {c_{0i} + {c_{1i}\frac{1}{f_{i}^{2}}} + {c_{2i}\frac{1}{f_{i}^{4}}}}},$

wherein c_(0i), c_(1i), and c_(2i), are mode dependent coefficients.

In a step 130, which is explained in greater detail below based on FIGS.2a and 2b , there occurs the determining of a suppressed excitationfrequency, which in a step 140 is set as value of the resonant frequencyf_(res) of the gas-charged liquid in the measuring tube.

In a step 150, there occurs based on the eigenfrequency f_(i) of themeasuring tube and the resonant frequency f_(res) the determining of adensity correction term for density measurement.

Finally, in a step 160, a corrected density value is determined by meansof the correction term.

FIG. 2a represents a first embodiment 130 a for the method step forascertaining the suppressed excitation frequency.

Oscillations are excited with a sequence of excitation frequencies 131 aover a frequency range, in which the suppressed excitation frequency isto be expected. In order to identify the frequency range, for example,based on the preliminary density and a reference value for density ofthe liquid, a rough estimate of the resonant frequency of the medium canoccur, wherein then a frequency range around the estimated value isselected. In similar manner, a resonant frequency can be estimated fromthe ratio of the eigenfrequencies, for example, of the f₁-mode and thef₃-mode.

For each of the excited frequencies, a frequency dependent oscillationamplitude is registered 132 a.

In the spectrum of the oscillation amplitudes produced in this way, thenan amplitude minimum is ascertained, which is identified as thesuppressed excitation frequency 133 a.

FIG. 2b represents a second embodiment 130 b for the method step forascertaining the suppressed excitation frequency.

Here, simultaneously, oscillations of all frequencies are excited withan excitation signal in the form of white noise 131 b, wherein thenoscillation deflection is registered as a function of time 132 b. AFourier transformation, especially FFT, 133 b transforms the time domaininto the frequency domain, wherein then such as described above anamplitude minimum as a function of frequency is ascertained andidentified as suppressed excitation frequency 134 b. For each of theexcited frequencies, a frequency dependent oscillation amplitude isregistered 132 a.

For determining the density correction term K_(i) as in step 150, theresonant frequency fres and the eigenfrequency fi applied forascertaining the preliminary density value are entered into thefollowing equation:

${K_{i}\mspace{14mu}\text{:=}\mspace{14mu}\left( {1 + \frac{r}{\left( \frac{f_{0}}{f_{i}} \right)^{2} - 1}} \right)},$

wherein f_(i) is the eigenfrequency of the not suppressed bendingoscillation mode, with which the preliminary ρ_(i) density measuredvalue was determined, and r is a constant, which, in this case, has thevalue 0.84.

The corrected density measured value ρ_(corr) is, finally, calculated inthe step 160 of the method in FIG. 1 according to:

$\rho_{corr} = \frac{\rho_{i}}{K_{i}}$

The preliminary density value ρ_(i) is, thus, divided by the correctionterm K_(i), in order to obtain the corrected density value ρ_(corr).

1-13. (canceled)
 14. A method for ascertaining a physical parameter of aliquid, which has a gas charge, wherein the gas is present especially inthe form of bubbles suspended in the liquid using a measuring transducerhaving at least one measuring tube for conveying the medium, wherein theat least one measuring tube has an inlet side end section and an outletside end section, wherein the measuring transducer has at least oneinlet side securement and one outlet-side securement, with which themeasuring tube is secured, in each case, in one of the end sections,wherein the measuring tube is excitable between the two securements toexecute oscillations in at least one bending oscillation mode, whereinthe method comprises steps as follows: exciting the measuring tube withan eigenfrequency of a bending oscillation mode, ascertaining asuppressed excitation frequency, at which the oscillation amplitude ofthe measuring tube is minimum, or disappears; identifying the suppressedexcitation frequency as the resonant frequency of the gas-chargedliquid; ascertaining a density correction term as a function of theresonant frequency for correcting a preliminary density measured valueor mass flow correction term as a function of the resonant frequency forcorrecting a preliminary mass flow rate measured value, or ascertainingthe velocity of sound in the gas-charged liquid in the measuring tube asa function of the resonant frequency.
 15. The method of claim 14,wherein the suppressed excitation frequency is ascertained by sampling afrequency range.
 16. The method of claim of claim 15, wherein thesampling of the frequency range comprises outputting excitation signalshaving a sequence of excitation frequencies in the frequency range forexciting measuring tube oscillations and registering frequency dependentoscillation amplitudes.
 17. The method of claim 14, wherein thesuppressed excitation frequency is ascertained by: exciting oscillationswith an excitation signal in the form of white noise; registeringresulting deflection of the measuring tube in the time domain;transforming the registration in the time domain into the frequencydomain; ascertaining frequency of an amplitude minimum; and identifyingthe ascertained frequency as the suppressed excitation frequency. 18.The method of claim 14, further comprising: ascertaining a preliminarydensity measured value or a preliminary mass flow rate measured value atthe eigenfrequency of the excited bending oscillation mode, andascertaining a corrected density measured value or a corrected mass flowrate measured value using the density correction term or the mass flowcorrection term, wherein the density correction term or the mass flowcorrection term are, or is, a function of the resonant frequency and theeigenfrequency of the excited bending oscillation mode, at which thepreliminary density measured value or the preliminary mass flow ratemeasured value were, or was, ascertained.
 19. The method of claim 14,wherein the density correction term K for a preliminary density value orthe mass flow correction term are, or is, a function of a quotient ofthe resonant frequency of the gas-charged liquid and the eigenfrequencyof the excited bending oscillation mode, at which the preliminarydensity measured value or mass flow rate measured value were, or was,ascertained.
 20. The method of claim 14, wherein the density correctionterm K for the preliminary density values ρ_(i) based on theeigenfrequency of the f_(i)-mode has the following form:${K_{i}\mspace{14mu}\text{:=}\mspace{14mu}\left( {1 + \frac{r}{\left( \frac{f_{res}}{f_{i}} \right)^{2} - b}} \right)},{wherein}$$\rho_{corr}\mspace{14mu}\text{·=}\mspace{14mu}\frac{\rho_{i}}{K_{i}}$wherein r is a median independent constant, f_(res) is the resonantfrequency of the gas-charged liquid, f_(i) is the eigenfrequency of theexcited bending oscillation mode, ρ_(corr), ρ_(i) are the corrected andthe preliminary densities, and b is a scaling constant.
 21. The methodof claim 14, wherein:r/b<1, especially r/b<0.9, wherein especially: b=1.
 22. The method ofclaim 14, wherein g is a proportionality factor between a resonantfrequency f_(res) of the gas-charged liquid and the velocity of sound inthe gas-charged liquid and depends on the diameter of the measuringtube, wherein thus, ${c = \frac{f_{res}}{g}},$ and a value of thevelocity of sound ascertained with the equation is output.
 23. Themethod of claim 14, wherein the preliminary density values aredetermined based on the eigenfrequency of the f_(i)-mode using apolynomial in 1/f_(i), wherein the coefficients of the polynomial aremode dependent.
 24. The method of claim 14, wherein a density errorE_(ρi) of a preliminary density value based on the eigenfrequency of thef_(i) mode is:E _(ρi) :=K _(i)−1, wherein a mass flow rate error E_(m) of apreliminary mass flow rate value is proportional to the density errorE_(ρ1) of the first preliminary density value, thus:E _(m) :=k·E _(ρ1), wherein the proportionality factor k amounts to notless than 1.9 and no more than 2.1, wherein the proportionality factor kespecially amounts to 2, wherein the mass flow correction term K_(m) forthe mass flow rate is:K _(m):=1+E _(m), wherein the corrected mass flow rate {dot over(m)}_(corr) is${{\overset{.}{m}}_{corr}\mspace{14mu}\text{·=}\mspace{14mu}\frac{{\overset{.}{m}}_{v}}{K_{m}}},$wherein {dot over (m)}_(v) is the preliminary mass flow rate value. 25.The method of claim 14, wherein the f₁-mode and the f₃-mode are excitedand their eigenfrequencies ascertained, and wherein as a function of theascertained eigenfrequencies a frequency range is established, in whichthe suppressed excitation frequency is to be sought.
 26. The method ofclaim 14, wherein a reference density is provided and wherein as afunction of the reference density and, in given cases, theeigenfrequency of the f₁-mode a frequency range is established, in whichthe suppressed excitation frequency is to be sought.